Research on Operational Safety Risk Assessment Method for Long and Large Highway Tunnels Based on FAHP and SPA

Abstract

Compared to the construction phase, the assessment of tunnel safety risks during the operational stage has not been thoroughly conducted, and the related research work is relatively lagging. To deepen the research and application of theoretical methods for assessing operational tunnel safety risks, and to improve the level of hazard investigation and prevention in long and large highway tunnels, this paper establishes a tunnel section assessment index system from four perspectives: tunnel condition, traffic characteristics, operational environment, and operational management. A combined qualitative and quantitative approach is employed, and a practical classification standard for the indicators is proposed. Based on the traditional Analytic Hierarchy Process (AHP) and fuzzy analysis theory, a new form of questionnaire survey, known as the expert system analysis method, is introduced to collect expert opinions. A novel approach for determining fuzzy numbers based on expert opinions is proposed. Consequently, a combined model for assessing operational tunnel safety risks in long and large highways is established by integrating the Fuzzy Analytic Hierarchy Process (FAHP) and the Set Pair Analysis (SPA). This model effectively combines subjective weighting with objective evaluation, thereby enhancing the accuracy of operational tunnel safety risk assessment for long and large highways. The safety risks of three long and large tunnels within the G1523 Yongguan Expressway were assessed using the evaluation method proposed in this paper. A comparative analysis was conducted between the results obtained using the proposed Fuzzy Analytic Hierarchy Process (FAHP) and Set Pair Analysis (SPA) method and the traditional Analytic Hierarchy Process (AHP) evaluation. The results indicate that the operational tunnel safety risk assessment method based on FAHP and SPA exhibits greater rationality and accuracy compared to the traditional AHP approach.

1. Introduction

With sustained investment in infrastructure construction in China and the continuous expansion of the national highway network into mountainous areas, the highway network is becoming increasingly well-developed. Simultaneously, there has been a rapid increase in the construction mileage of tunnels along the highways. By the end of 2022, there were a total of 24,850 highway tunnels in China, spanning a length of 26,784.3 km. Among them, 1752 tunnels classified as extra-long, with a total length of 7951.1 km, and 6715 tunnels were classified as long, with a total length of 11,728.2 km. China has become the country with the highest number of road tunnels and the longest tunnel mileage in the world, but the associated operational risks of these road tunnels have also become a serious concern [1]. Liu Songrong et al. [2] conducted a statistical analysis of nearly 80,000 tunnel incidents and accidents that occurred in 58 tunnels in a certain province of China between 2019 and 2021. They found that longer tunnels were associated with a higher number of accidents. By reviewing relevant domestic and international data and literature, the main causes of operational risks in large highway tunnels were summarized as follows:

(1)

Many operational highway tunnels still exhibit historical deficiencies inherited from their design and construction phases. During the operation process, the increasing vulnerability of these tunnels at specific locations highlights the emergence of safety risks for their subsequent management.

(2)

The current state of highway tunnel operation and management in China is characterized by weak operational management, lack of management information, inadequate safety facility provisions, inadequate maintenance, blind spots in monitoring and sensing facilities, incomplete disaster response plans, and challenges in addressing overloading and over-limiting issues. These factors contribute to an unsatisfactory tunnel operational safety situation.

(3)

The enclosed and narrow space within tunnels restricts the evacuation of trapped individuals and imposes greater limitations on emergency rescue operations. Traffic accidents resulting in multiple casualties and injuries, such as chain-reaction collisions, fires induced by primary accidents, and leaks of hazardous materials, still occur in long and large tunnels during their operational phase.

Risk management refers to the management process of minimizing potential losses and negative impacts caused by risks in an inherently risky environment. In the 1970s, the United States took the lead in introducing risk theory in the field of tunnel and underground engineering and proposed characteristics and methods of risk analysis for underground engineering. Subsequently, scholars from various countries gradually integrated the theory of risk with railway and highway tunnels as well as metro construction projects, applying it to the planning, design, construction, and operation of engineering projects. During the operational phase of engineering projects, highway tunnels are more susceptible to accidents and have greater risks compared to underground engineering projects such as metro and railway tunnels. This is due to the influence of external environmental factors and higher levels of uncertainty. In 1999, significant fires occurred in the Mont Blanc Tunnel in Italy and the Tauern Tunnel in Austria, resulting in devastating losses. Subsequently, European countries developed the EuroTAP program, with the German ADAC and British AA organizations as operational centers, and established the EuroTest institution to conduct an assessment and evaluation of the risk situation of existing highway tunnels in Europe. In this context, the European Commission initiated Directive 2004/54/EC, and EU member states, considering their characteristics, issued risk analysis methods applicable to their specific contexts, as shown in

Table 1. Risk analysis methods for EU member states.

Country	Risk Analysis Methods
France	Based on specific disaster scenarios, quantitative models are established for risk analysis.
Norway	A model is established to calculate the likelihood (accident frequency) of traffic accidents occurring at different locations within the tunnel.
Netherlands	By conducting an optimized analysis of the entire accident process, the vulnerable areas of the tunnel system are identified.
Britain	By employing the evaluation scale of “risk priority number”, the likelihood and consequences of accidents are assessed and evaluated.
Italy	The expected probability of design accidents and the simulated consequences are calculated to determine tunnel risks.

[3]. Outside of Europe and the Americas, countries such as Singapore have adopted the Quantitative Risk Assessment of Freeway Tunnels (QRAFT) model for their unique highway tunnels. This model enables the identification of potential hazards and provides an analysis of the probability of occurrence and potential consequences associated with these hazards [4].

Due to concerns about tunnel operational safety, numerous scholars have conducted research on tunnel risk management using various methods. Caliendo et al. [5,6] performed regression analysis on historical accident data from highway tunnels over a certain period to investigate accident characteristics and the inherent relationships between these characteristics and various influencing factors related to tunnel infrastructure and the driving environment. The goal was to identify proactive improvements in tunnel infrastructure and traffic conditions to suppress the occurrence of traffic accidents. Meanwhile, numerous scholars have proposed several accident prediction models through the analysis and simulation of accidents. For instance, Caliendo et al. [7] analyzed the annual effects of severe accidents using a random-effects logistic regression model and a negative binomial regression model and developed a collision prediction model for highway tunnels. Yamamoto K [8] utilized Fire Dynamics Simulator (FDS) fire simulation software to replicate tunnel fires and employed the Real-coded Cellular Automata (RCA) method to simulate the evacuation process. The study investigated the impact of tunnel wind speed and the number of evacuees on evacuation time. Ntzeremes P [9] proposed an enhanced evacuation simulation model for quantitative risk assessment of highway tunnel fires. This model aims to improve the efficiency of quantitative risk assessment by estimating the potential losses of trapped individuals inside the tunnel. Luo Q [10] based their study on traffic accident data from Pennsylvania between 1997 and 2020 to identify the characteristics and trends of road closure duration resulting from tunnel traffic accidents.

In recent years, Chinese scholars have conducted extensive research on the analysis of highway tunnel accidents and safety evaluations. Their work has provided valuable methods and insights for the assessment of tunnel operational risks. Wang Qian [11], Xue Feng [12], Duan Ruyu [13], and others combined the current status of Chinese highway tunnel operation management and the characteristics of tunnel traffic accidents to conduct a comprehensive analysis of various factors influencing tunnel operational safety. They integrated the Delphi method, Analytic Hierarchy Process (AHP), and Decision-Making Trial and Evaluation Laboratory (DEMATEL) method and established a tunnel operational safety evaluation index system and a level classification calculation model. They also constructed quantitative analysis standards for the evaluation index system and indicators, providing a basis for tunnel operational safety risk assessment. At the same time, some scholars have started to apply risk theory to tunnel engineering practices and use it as a basis to explore and establish the inherent connections between the two. Zhao Feng [14] conducted a statistical analysis of domestic and international accident data and characteristic patterns of in-service highway tunnels. For the first time, he proposed the Tunnel Operational Social Risk Acceptance Criteria (F-N curve) specifically for China. Hu Jiawei [15] and others combined the characteristics and hazards of highway tunnel fires from both domestic and international sources. They utilized the Interpretive Structural Modeling (ISM) to analyze the hierarchical relationships among various factors and established a four-level hierarchical structure. This allowed them to conduct a qualitative analysis of the causes of highway tunnel fire incidents. Li Qian [16] and others conducted a study on highway tunnel traffic accidents in the southwestern mountainous region of China. They introduced the accident tree analysis method and quantified the importance of accident safety factors through structural importance analysis. Currently, in China, research on tunnel operational risk assessment methods mostly involves comprehensive integration or improvement of methods that have been applied in other engineering fields. Wu Senyang et al. [17], building upon the risk parameters of EuroTAP for highway tunnel operation, expanded the evaluation scope and accuracy and established a highway tunnel operation safety level assessment method suitable for the Chinese context. Yuan Jiawei [18] employed Analytic Hierarchy Process (AHP), Fuzzy Comprehensive Evaluation (FCE) method, and the Extension Theory-based Comprehensive Evaluation (ETCE) method to assess the risks of highway tunnels in Sichuan Province, China. After conducting a comparative analysis, they identified the most suitable and rational evaluation method and applied it to the engineering project. Zhou Bing [19] and others, based on the Maluanshan Tunnel project, proposed an urban traffic tunnel operational safety risk assessment system that combines overall evaluation and specific assessment.

Currently, tunnel operation safety management in China primarily relies on a “reactive approach”, focusing on “response during an emergency after incidents”. However, research on theoretical methods and control technologies for “prevention before incidents” is significantly lagging. Compared with the advanced safety management theories and practices in domestic and international contexts, the construction of a comprehensive risk management system for highway tunnel operation safety in the transportation industry is not yet fully developed. There are still many gaps and deficiencies in operational safety management. Therefore, researching operational risk assessment for long and large highway tunnels, promoting the establishment of tunnel safety risk management systems, and enhancing the tunnel’s resilience against risks are pressing tasks. Based on previous research, this paper focuses on the characteristics of long and large highway tunnels. A questionnaire survey involving experts was conducted to quantify the fuzzy characteristics of risk factors. The triangular fuzzy Analytic Hierarchy Process (FAHP) was employed to determine the fuzzy weight of evaluation indicators. In addition, the Set Pair Analysis (SPA) was utilized to compare the membership relationship between the indicator set and the standard set, thereby determining the rating range of evaluation indicators. Consequently, a comprehensive highway long and large tunnel operational safety risk assessment model was established by combining subjective and objective approaches.

2. Construction of the Evaluation Indicator System

2.1. Segmentation of Tunnel Sections

In the research conducted by scholars both domestically and internationally on the distribution of accidents in tunnel sections, a common practice is to divide the tunnel into five zones based on the differences in the operating environment characteristics and driver behavior. These zones include the tunnel entrance transition zone, entrance zone, tunnel interior, exit zone, and exit transition zone [20]. Yuan Jiawei [18] classified tunnel accidents based on accident locations and conducted a statistical analysis of tunnel accident data within four routes in Sichuan Province, China. The analysis revealed that accidents were predominantly concentrated within a 200 m range near the tunnel portals. Yeung J.S. and colleagues [21] conducted a study that revealed a significant variation in the accident rate along the range of 50 to 200 m from tunnel portals on highways. To include all accidents that may be related to tunnel factors in the statistics and provide a certain safety margin, this paper defines the portal section length as extending 250 m inward and outward from the tunnel portal, as depicted in Figure 1. This length effectively covers the region where the accident rate at the tunnel portal exhibits significant changes. Additionally, the selection of a 250 m length ensures that the actual characteristics of the portal transition section are not overshadowed by an excessively averaged accident rate.

Highway long tunnels exhibit distinct characteristics in different sections of their operational environment. There are significant differences between the tunnel entrance section and the middle section in terms of the operational environment. Therefore, when conducting an operational risk assessment, it is necessary to determine the respective focuses for each section based on their operational characteristics and establish corresponding assessment indicator systems. The features of each section’s grading criteria should be determined based on the environmental characteristics of different sections. In this paper, based on the previously defined length of the tunnel entrance section, the entire evaluation section of the tunnel is divided into the entrance section (segments A and B), the middle section (segment C), and the exit section (segments D and E), as shown in Figure 2, for tunnel operational safety risk assessment.

2.2. Selection of Evaluation Indicators

To comprehensively consider the influencing factors of tunnel operation risk, a multi-level comprehensive evaluation indicator system is introduced. Due to the difficulty in quantifying human unsafe behaviors and vehicle unsafe conditions, and based on the analysis of the causes of traffic accidents, it is evident that a significant portion of accidents is indirectly induced by factors such as road conditions, environment, and management. These factors then manifest through human and vehicle factors as the apparent cause of the accidents. Therefore, this study refers to relevant laws, regulations, and research findings from domestic and foreign scholars [22,23,24] as the basis. Through methods such as on-site investigations, expert consultations, and frequency statistics, the study identifies and selects indicators primarily from four aspects: “tunnel condition, traffic characteristics, operational environment, and operational management.” Considering the notable differences in the operational environment between the tunnel portal section and the tunnel mid-section, the study constructs a highway long and large tunnel operational safety risk assessment index system, as depicted in Figure 3.

2.3. Indicator Grading Criteria

Based on the risk assessment indicator system determined in Figure 3 and considering the operational safety requirements for the tunnel entrance segment and the middle segment, the safety risk levels of each indicator were classified into five levels. This classification was established based on the current design standards and specifications in China and was informed by relevant research findings from both domestic and international sources. The corresponding grading criteria have been determined and are presented in

Table 2. Grading Criteria for Risk Assessment Indicator System.

Risk Level			Low	Relatively Low	Medium	Relatively High	High
Tunnel Condition Indicators	Civil Engineering Structural Techniques (Score)		≥85	[70,85)	[55,70)	[40,55)	<40
	Electromechanical Facilities Technical Condition (Score)		≥98	[95,98)	[91,95)	[81,91)	<81
	Technical Condition of Other Facilities (Score)		≥85	[70,85)	[55,70)	[40,55)	<40
	Tunnel Length (m)		<1000	[1000,3000)	[3000,6000)	[6000,10,000)	≥10,000
	Length of Tunnel Entrance Transition Section (m)		≥5 V	[3 V,5 V)	[2 V,3 V)	[V,2 V)	<V
	Minimum Radius of Planar Curve (m)	80 km/h	≥2500	[1500,2500)	[700,1500)	[400,700)	<400
		100 km/h	≥4000	[2000,4000)	[1100,2000)	[700,1100)	<700
	Maximum Slope (%)		(0.3,1]	(1,2]	(2,2.5]	(2.5,3]	>3
	Pavement Quality Index (PQI)		≥90	[80,90)	[70,80)	[60,70)	<60
	Sideways Force Coefficient (SFC)	Concrete pavement	≥56	[46,56)	[39,46)	[31,39)	[0,31)
		Asphalt pavement	≥61	[51,61)	[41,51)	[31,41)	[0,31)
	Provision of cross passages and emergency stopping lanes (score)		[80,100]	[60,80)	[40,60)	[20,40)	[0,20)
Indicators of traffic characteristics	Operating speed $\left|V_{85}-V_0\right|$ (km/h)		≤5	(5,10]	(10,15]	(15,20]	>20
	Coordinated nature of operating speeds $\left|\mathsf{\Delta }{V}_{85}\right|$ (km/h)		≤7	(7,10]	(10,15]	(15,20]	>20
	Coefficient of variation of vehicle speed		≤0.1	(0.1,0.15]	(0.15,0.20]	(0.20,0.25]	>0.25
	Service level (V/C)		≤0.2	(0.2,0.3]	(0.3,0.4]	(0.4,0.5]	(0.5,0.6]
			>0.9	(0.8,0.9]	(0.7,0.8]	(0.6,0.7]	(0.5,0.6]
	Overload ratio (%)		≤0.5	(0.5,3.0]	(3.0,5.0]	(5.0,10.0]	>10.0
	Proportion of large vehicles (%)		≤20	(20,25]	(25,30]	(30,40]	(40,60]
			>80	(75,80]	(70,75]	(60,70]	(40,60]
Operational environment indicators	CO concentration (cm3/m3)		≤70	(70,100]	(100,150]	(150,200]	>200
	Visibility	Attenuation coefficient K (10−3 m−1)	≤5.0	(5.0,7.0]	(7.0,9.0]	(9.0,12.0]	>12.0
		Meteorological visibility (km)	≥0.5	[0.2,0.5)	[0.1,0.2)	[0.05,0.1)	<0.05
	Luminance	Enhanced lighting in transition sections	≥13.0	[11.0,13.0)	[9.0,11.0)	[7.0,9.0)	<7.0
		General illumination	≥8.0	[6.0,8.0)	[4.0,6.0)	[2.0,4.0)	<2.0
	Noise decibel value (dB)		≤75	(75,85]	(85,90]	(90,95]	>95
	Proportion of adverse weather (%)		≤10	(10,30]	(30,50]	(50,70]	>70
Operations management	Organizational structure (score)		[80,100]	[60,80)	[40,60)	[20,40)	[0,20)
	Regulations and procedures (score)		[80,100]	[60,80)	[40,60)	[20,40)	[0,20)
	Education and training (score)		[80,100]	[60,80)	[40,60)	[20,40)	[0,20)
	Emergency management (score)		[80,100]	[60,80)	[40,60)	[20,40)	[0,20)
	Traffic management (score)		[80,100]	[60,80)	[40,60)	[20,40)	[0,20)

.

Qualitative indicators, such as the level of emergency management, which are difficult to quantify but have an impact on operational safety, were categorized into five risk levels ranging from low to high. To provide a quantitative representation of these qualitative indicators, a corresponding numerical scale was established, consisting of five interval values: 80–100, 60–80, 40–60, 20–40, and 0–20. Based on the subjective judgments of experts, the evaluated indicators were scored to roughly represent their impact on tunnel operational safety.

3. Construction of the Risk Assessment Model

Given the application status of risk assessment techniques in tunnel safety risk assessment in China, considering the difficulty in obtaining objective data in reality and the inherent difficulty in quantifying certain risk factors due to their fuzzy nature, this paper proposes a comprehensive evaluation method based on the principles of the traditional Analytic Hierarchy Process (AHP) and Fuzzy Comprehensive Evaluation. The proposed method utilizes the Triangular Fuzzy Analytic Hierarchy Process (FAHP) to combine subjective weighting with objective evaluation, aiming to improve the accuracy of the assessment approach.

On the subjective level, expert opinions are collected through a questionnaire survey to quantify the fuzzy characteristics of risk factors. The Triangular Fuzzy Analytic Hierarchy Process (FAHP) is employed to determine the fuzzy weights of evaluation criteria. On the objective level, the Set Pair Analysis (SPA) method is utilized to compare the membership relationships between the indicator set and the standard set, thereby determining the ranking range of evaluation criteria. Finally, by combining the subjective and objective approaches, the overall risk level of tunnel operational safety is determined.

3.1. Expert Questionnaire Survey

3.1.1. Traditional Expert Questionnaire Survey

Traditional expert survey questionnaires utilize pairwise comparisons among evaluation criteria within a certain criterion to calculate the relative importance weights of the indicators at that level concerning the higher-level membership criterion. The specific form of this calculation is illustrated in Figure 4.

When evaluating extensive indicator systems, the traditional expert questionnaire surveys require a significant number of pairwise comparisons between factors, resulting in a laborious and time-consuming process. Moreover, the constructed comparison judgment matrix may not guarantee consistency. Based on the current application status of this method, this paper introduces a new questionnaire survey method and combines it with Triangular Fuzzy Analytic Hierarchy Process (FAHP) to enhance the manipulability of the assessment method and improve the accuracy of evaluation results.

3.1.2. Expert System Analysis Method

To obtain expert opinions quickly and effectively, scholar Lyu H. M. [25] proposed a new questionnaire survey method based on the traditional expert questionnaire survey. This method utilizes a quantification scale of 1 to 9 to assess the impact of lower-level factors on upper-level membership factors. During the implementation process, it is crucial to ensure that scores assigned to each element in each layer are unique and non-repetitive. In practical applications, it is possible to establish specific evaluation criteria corresponding to different indicator systems, primarily aiming to prioritize evaluation factors based on their level of influence. This approach allows for the prioritized ranking of evaluation indicators according to their impact. The questionnaire survey of this form is simple and clear, enabling decision-makers to intuitively compare and prioritize various indicator factors. The specific content and format of the questionnaire can be found in Figure 5.

3.2. Triangular Fuzzy Analytic Hierarchy Process

Based on experts’ experience and preferences, the traditional approach provides a single numerical value, overlooking the impact of cognitive differences among decision-makers and the presence of fuzziness and uncertainty in the judgment process, resulting in a high degree of subjectivity in the indicator weights. To address this, fuzzy mathematics employs fuzzy numbers to represent the relative importance of evaluation indicators, reducing the influence of subjective factors. In this paper, based on the expert system analysis approach, triangular fuzzy numbers are utilized to replace single numerical values and derive the weights of indicators.

3.2.1. Introduction to Triangular Fuzzy Numbers

For a fuzzy number “M” defined on the real domain R, if its membership function is expressed as [26]:

$$\begin{array}{l}{\mathsf{\mu }}_{\mathrm{M}}\left(\mathrm{x}\right)=\left\{\begin{array}{l}0 (\mathrm{x}<\mathrm{l})\\ \frac{\mathrm{x}-\mathrm{l}}{\mathrm{m}-\mathrm{l}} (\mathrm{l}\le \mathrm{x}<\mathrm{m})\\ \frac{\mathrm{u}-\mathrm{x}}{\mathrm{u}-\mathrm{m}} (\mathrm{m}\le \mathrm{x}<\mathrm{u})\\ 0 (\mathrm{x}\ge \mathrm{u})\end{array}\right.\\ \end{array}$$

(1)

In the equation, if μ_M (x) ∈ [0,1], x ∈ R, the fuzzy number M is referred to as a triangular fuzzy number, denoted as M = (l, m, u) (l ≤ m ≤ u). Here, l, u, and m respectively represent the lower bound, upper bound, and the most plausible value within the possibility interval. The triangular fuzzy distribution is illustrated in Figure 6, and when l = u = m, M becomes a crisp (precise) number. While the traditional Analytic Hierarchy Process (AHP) is straightforward and easy to use, its representation of subjective decisions using a single numerical value limits the accuracy of evaluations to some extent. Triangular fuzzy numbers express a range of possibilities, and the accuracy of the Triangular Fuzzy Analytic Hierarchy Process (FAHP) does not lie in quantifying fuzzy problems in advance but rather in preserving fuzziness to the maximum extent during mathematical operations [27].

3.2.2. Construction of the Hierarchy Structure

Based on the overall objective of the evaluation, and through a comprehensive analysis of various risk sources and influencing factors in complex systems, a hierarchical structure is established for the system, as shown in Figure 7.

3.2.3. Construction of Triangular Fuzzy Judgment Matrix

Using the expert system analysis approach, expert opinions are collected and then filtered and aggregated. Following the principles of the Analytic Hierarchy Process (AHP), pairwise comparison matrices A_r,k are determined to assess the importance of indicators at each level. The corresponding comparison matrices for each level, based on expert opinions, are summed and averaged to obtain the average comparison matrix A_r. By interpreting the tendency information carried by the numerical values in the average matrix A_r, simplified triangular fuzzy numbers are used to represent the ratios. Based on this, the corresponding simplified triangular fuzzy judgment matrix is constructed as shown in Equation (2).

$${\mathrm{R}}_{\mathrm{N}}=\left[\begin{array}{cccc}1& {\tilde{\mathrm{r}}}_{12}& \mathrm{L}& {\tilde{\mathrm{r}}}_{1\mathrm{n}}\\ {\tilde{\mathrm{r}}}_{21}& 1& \mathrm{L}& {\tilde{\mathrm{r}}}_{2\mathrm{n}}\\ \mathrm{M}& \mathrm{M}& \mathrm{O}& \mathrm{M}\\ {\tilde{\mathrm{r}}}_{\mathrm{n}1}& {\tilde{\mathrm{r}}}_{\mathrm{n}2}& \mathrm{L}& 1\end{array}\right]$$

(2)

The values of simplified triangular fuzzy numbers should closely reflect the importance information contained in the ${\mathrm{U}}_{\mathrm{i}}{/\mathrm{U}}_{\mathrm{j}}$ and ${\mathrm{U}}_{\mathrm{j}}{/\mathrm{U}}_{\mathrm{i}}$ of the average comparison matrix A_r. The resulting simplified triangular fuzzy judgment matrix should satisfy consistency. According to the matrix definition, in Equation (2), ${\tilde{\mathrm{r}}}_{\mathrm{ij}}$ represents the fuzzy ratio of the importance level between factor x_i and factor x_j, and its values are still represented using 1, 2, 3, …9.

By using triangular fuzzy numbers instead of their corresponding simplified triangular fuzzy numbers, and based on the obtained triangular fuzzy judgment matrix, the weights of evaluation criteria can be determined. In this context, the simplified triangular fuzzy number $\tilde{\mathrm{r}}$.

$\tilde{\mathrm{r}}$ represents “approximately equal to r”, and its specific definition is presented in

Table 3. Triangular fuzzy numbers and their meanings.

Comparison of the Importance between xi and xj	Equal Importance	Equal Importance	Moderately Important	Strongly Important	Highly Important	In Between
${\tilde{\mathrm{r}}}_{\mathrm{ij}}$ Simplified triangular fuzzy numbers	1	3	5	7	9	2,4,6,8
${\mathrm{r}}_{\mathrm{ij}}$ Triangular fuzzy numbers	(1,1,2)	(2,3,4)	(4,5,6)	(6,7,8)	(8,9,9)	$\left({\mathrm{r}}_{\mathrm{ij}}-{1,\mathrm{r}}_{\mathrm{ij}}{,\mathrm{r}}_{\mathrm{ij}}+1\right)$

Note: ${\tilde{\mathrm{r}}}_{\mathrm{ji}}$ represents the fuzzy ratio of the importance degree of factor x_j to factor x_i. ${\tilde{\mathrm{r}}}_{\mathrm{ji}}=\frac{1}{{\tilde{\mathrm{r}}}_{\mathrm{ij}}}$ indicates an equal importance, and similarly, ${\mathrm{r}}_{\mathrm{ji}}=\frac{1}{{\mathrm{r}}_{\mathrm{ij}}}=\left(\frac{1}{{\mathrm{r}}_{\mathrm{ij}}+1},\frac{1}{{\mathrm{r}}_{\mathrm{ij}}},\frac{1}{{\mathrm{r}}_{\mathrm{ij}}-1}\right)$ holds.

[28]. For a given fuzzy judgment matrix, if the matrix composed of its simplified triangular fuzzy numbers satisfies the consistency requirements, it can be approximately considered that the triangular fuzzy judgment matrix also satisfies the consistency requirements.

By substituting triangular fuzzy numbers, a triangular fuzzy judgment matrix can be constructed as shown in Equation (3).

$$\begin{array}{l}{\mathrm{R}}_{\mathrm{N}}={\left({\mathrm{l}}_{\mathrm{ij}}{,\mathrm{m}}_{\mathrm{ij}}{,\mathrm{u}}_{\mathrm{ij}}\right)}_{\mathrm{n}\times \mathrm{n}}\\ =\left(\begin{array}{cccc}\left[1,1,1\right]& \left[{\mathrm{l}}_{12}{,\mathrm{m}}_{12}{,\mathrm{u}}_{12}\right]& \mathrm{L}& \left[{\mathrm{l}}_{1\mathrm{n}}{,\mathrm{m}}_{1\mathrm{n}}{,\mathrm{u}}_{1\mathrm{n}}\right]\\ \left[\frac{1}{{\mathrm{u}}_{12}},\frac{1}{{\mathrm{m}}_{12}},\frac{1}{{\mathrm{l}}_{12}}\right]& \left[1,1,1\right]& \mathrm{L}& \left[{\mathrm{l}}_{2\mathrm{n}}{,\mathrm{m}}_{2\mathrm{n}}{.\mathrm{u}}_{2\mathrm{n}}\right]\\ \mathrm{M}& \mathrm{M}& \mathrm{O}& \mathrm{M}\\ \left[\frac{1}{{\mathrm{u}}_{1\mathrm{n}}},\frac{1}{{\mathrm{m}}_{12}},\frac{1}{{\mathrm{l}}_{1\mathrm{n}}}\right]& \left[\frac{1}{{\mathrm{u}}_{2\mathrm{n}}},\frac{1}{{\mathrm{m}}_{2\mathrm{n}}},\frac{1}{{\mathrm{l}}_{2\mathrm{n}}}\right]& \mathrm{L}& \left[1,1,1\right]\end{array}\right)\end{array}$$

(3)

3.2.4. Calculation of Single-Level Indicator Weights

Based on the obtained triangular fuzzy matrix, the overall fuzziness of each factor is computed. Let M_ij denote the value of factor i relative to factor j in the triangular fuzzy matrix. The comprehensive fuzziness of the i-th factor is then given by:

$${\mathrm{P}}_{\mathrm{i}}={\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{M}}_{\mathrm{ij}}}\otimes {\left({\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{M}}_{\mathrm{ij}}}}\right)}^{-1}$$

(4)

In the equation, $\otimes$ represents the multiplication of two triangular fuzzy numbers. ${\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{M}}_{\mathrm{ij}}}$ and ${\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{M}}_{\mathrm{ij}}}}$ represent the summation operation of triangular fuzzy numbers, which can be obtained using Equations (5) and (6), respectively.

$${\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{M}}_{\mathrm{ij}}}=\left({\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{l}}_{\mathrm{ij}},}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{m}}_{\mathrm{ij}},}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{u}}_{\mathrm{ij}}}\right)$$

(5)

$${\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{M}}_{\mathrm{ij}}}}=\left({\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{l}}_{\mathrm{ij}},{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{m}}_{\mathrm{ij}},}}}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{u}}_{\mathrm{ij}}}}\right)$$

(6)

Correspondingly, ${\left({\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{M}}_{\mathrm{ij}}}}\right)}^{-1}=\left(\frac{1}{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{u}}_{\mathrm{ij}}}}},\frac{1}{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{m}}_{\mathrm{ij}}}}},\frac{1}{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{l}}_{\mathrm{ij}}}}}\right)$ can be obtained.

By calculating the above equation, the comprehensive fuzziness of each factor can be obtained. Assuming that ${\mathrm{P}}_1=\left({\mathrm{l}}_1{,\mathrm{m}}_1{,\mathrm{u}}_1\right)$ and ${\mathrm{P}}_2=\left({\mathrm{l}}_2{,\mathrm{m}}_2{,\mathrm{u}}_2\right)$ are the comprehensive fuzziness of two factors. Then, the possibility degree of ${\mathrm{P}}_1\ge {\mathrm{P}}_2$ can be defined as follows:

$$\mathsf{\mu }\left({\mathrm{P}}_1\ge {\mathrm{P}}_2\right){ = \sup }_{\mathrm{y}\ge \mathrm{x}}\left[\min \left({\mathsf{\mu }}_{{\mathrm{P}}_1}\left(\mathrm{x}\right){,\mathsf{\mu }}_{{\mathrm{P}}_2}\left(\mathrm{x}\right)\right)\right]$$

(7)

The geometric interpretation of the possibility degree of ${\mathrm{P}}_1\ge {\mathrm{P}}_2$ is shown in Figure 8, where the overlapping area of the two triangles represents the confidence level of fuzzy judgment, and its value can be represented by $\mathsf{\mu }\left({\mathrm{P}}_1\ge {\mathrm{P}}_2\right)$. The calculation formula is as follows:

$$\mathsf{\mu }\left({\mathrm{P}}_1\ge {\mathrm{P}}_2\right)=\left\{\begin{array}{l}1 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{m}}_1\ge {\mathrm{m}}_2\right)\\ \frac{{\mathrm{l}}_2{-\mathrm{u}}_1}{\left({\mathrm{m}}_1{-\mathrm{u}}_1\right)-\left({\mathrm{m}}_2{-\mathrm{l}}_2\right)} \left({\mathrm{m}}_1<{\mathrm{m}}_2{,\mathrm{l}}_2<{\mathrm{u}}_1\right) \\ 0 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(\mathrm{other}\right)\end{array}\right.$$

(8)

Similarly, based on the equation above, the following matrix of possibility degrees can be obtained:

$$\mathsf{\mu }\left(\mathrm{d}\right)=\left(\begin{array}{cccc}1& \mathsf{\mu }\left({\mathrm{P}}_1\ge {\mathrm{P}}_2\right)& \mathrm{L}& \mathsf{\mu }\left({\mathrm{P}}_1\ge {\mathrm{P}}_{\mathrm{n}}\right)\\ \mathsf{\mu }\left({\mathrm{P}}_2\ge {\mathrm{P}}_1\right)& 1& \mathrm{L}& \mathsf{\mu }\left({\mathrm{P}}_2\ge {\mathrm{P}}_{\mathrm{n}}\right)\\ \mathrm{M}& \mathrm{M}& \mathrm{O}& \mathrm{M}\\ \mathsf{\mu }\left({\mathrm{P}}_{\mathrm{n}}\ge {\mathrm{P}}_1\right)& \mathsf{\mu }\left({\mathrm{P}}_{\mathrm{n}}\ge {\mathrm{P}}_2\right)& \mathrm{L}& 1\end{array}\right)$$

(9)

Let $\mathsf{\mu }\left({\mathrm{d}}_{\mathrm{i}}\right)$ represent the weight component of factor i in the current layer. Then, the weight vector of evaluation indicators in the current layer, denoted as w_o, can be represented as ${\mathrm{w}}_{\mathrm{o}}=\left(\mathsf{\mu }\left({\mathrm{d}}_1\right),\mathsf{\mu }\left({\mathrm{d}}_2\right),\mathrm{L},\mathsf{\mu }\left({\mathrm{d}}_{\mathrm{n}}\right)\right)$, and its value can be calculated using Equation (10).

$$\mathsf{\mu }\left({\mathrm{d}}_{\mathrm{i}}\right)=\mathsf{\mu }\left({\mathrm{P}}_{\mathrm{i}}\ge {\mathrm{P}}_1{,\mathrm{P}}_{\mathrm{i}}\ge {\mathrm{P}}_2,\dots {,\mathrm{P}}_{\mathrm{i}}\ge {\mathrm{P}}_{\mathrm{n}}\right)=\min \left[\mathsf{\mu }\left({\mathrm{P}}_{\mathrm{i}}\ge {\mathrm{P}}_{\mathrm{k}}\right),\mathrm{k}=1,2,\dots ,\mathrm{n},\mathrm{k}\ne \mathrm{i}\right]$$

(10)

After normalizing the weight vector w_o using Equation (11), we obtain $\mathrm{w}=\left(\mathsf{\mu }{\left({\mathrm{d}}_1\right)}^{\prime },\mathsf{\mu }{\left({\mathrm{d}}_1\right)}^{\prime },\mathrm{L},\mathsf{\mu }{\left({\mathrm{d}}_{\mathrm{n}}\right)}^{\prime }\right)$, where ${\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\mathsf{\mu }{\left({\mathrm{d}}_{\mathrm{i}}\right)}^{\prime }}=1$.

$$\mathsf{\mu }{\left({\mathrm{d}}_{\mathrm{i}}\right)}^{\prime }=\frac{\mathsf{\mu }\left({\mathrm{d}}_{\mathrm{i}}\right)}{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\mathsf{\mu }\left({\mathrm{d}}_{\mathrm{i}}\right)}}$$

(11)

The magnitude of the single-layer indicator weights can be calculated through the above steps.

3.2.5. Comprehensive Ranking Weights

Based on the relative weights of each indicator, the method of hierarchical weighted summation is adopted to combine the weights of each layer, resulting in the comprehensive ranking weights of factors relative to the target layer. By utilizing the aforementioned method to calculate the weights of the evaluation indicators, both the influence of different expert decisions and the fuzziness of subjective judgments are taken into consideration through the use of triangular fuzzy numbers. This approach ensures that the obtained weights of the evaluation indicators are closer to objective reality.

3.3. Set Pair Analysis Method

The Set Pair Analysis (SPA) is essentially a process of analyzing the measured values of indicators and pre-set evaluation criteria through set pair analysis. The central idea is to perform analyses of similarity, opposition, and difference in the characteristics of a set pair I = (A, B) within a certain context, establishing the identical discrepancy contrary (IDC) of the set pair. The scholars [29,30] proposed that the improved Set Pair Analysis (SPA) is an extension and generalization of the identical discrepancy contrary (IDC) in traditional set pair analysis. It not only simplifies the evaluation process of entities but also enhances the reliability of quantitative research to some extent. In this paper, an improved set pair analysis model will be applied to determine the degree of convergence between evaluation indicators and evaluation levels.

3.3.1. Comprehensive Ranking Weights

In the context of risk assessment for determining risk levels, it is necessary to establish the association between the measured values of indicators and the criteria for evaluation levels. In this paper, the degree of association μ_k is determined based on the numerical closeness between the measured values of indicators and the criteria for evaluation levels. Accordingly, a corresponding calculation system is established.

Assuming that the evaluation criteria for the indicator i are divided into N levels, the identical discrepancy contrary between the measured value x_i of the indicator and the reference level k is illustrated in Figure 9. The degree of association μ_ik is 1 when x_i falls within the range of level k. If x_i is within the range of adjacent level criteria, μ_ik ∈ [–1,1]. However, if x_i falls within the range of non-adjacent level criteria, μ_ik = −1. According to the above definition, the degree of association μ_ik between evaluation indicator i and reference level k can be calculated using Equation (12):

$${\mathsf{\mu }}_{\mathrm{ik}}=\left\{\begin{array}{l}1-2\left|\frac{{\mathrm{p}}_{\mathrm{i},\mathrm{k}-1}-{\mathrm{x}}_{\mathrm{i}}}{{\mathrm{p}}_{\mathrm{i},\mathrm{k}-1}-{\mathrm{p}}_{\mathrm{i},\mathrm{k}-2}}\right|\hspace{1em}\hspace{1em}\left({\mathrm{If} \mathrm{x}}_{\mathrm{i}} \mathrm{belongs} \mathrm{to} \mathrm{level} \mathrm{k}-1\right) \\ 1 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{If} \mathrm{x}}_{\mathrm{i}} \mathrm{belongs} \mathrm{to} \mathrm{level} \mathrm{k}\right)\\ 1-2\left|\frac{{\mathrm{x}}_{\mathrm{i}}-{\mathrm{p}}_{\mathrm{i},\mathrm{k}}}{{\mathrm{p}}_{\mathrm{i},\mathrm{k}+1}-{\mathrm{p}}_{\mathrm{i},\mathrm{k}}}\right|\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{If} \mathrm{x}}_{\mathrm{i}} \mathrm{belongs} \mathrm{to} \mathrm{level} \mathrm{k}+1\right) \\ -1 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{If} \mathrm{x}}_{\mathrm{i}} \mathrm{belongs} \mathrm{to} \mathrm{another} \mathrm{level}\right)\end{array}\right.$$

(12)

In the equation, x_i represents the measured value of indicator i, and p_{i, k} represents the threshold value corresponding to indicator i for level k, where k = 1, 2, …, N represents the risk level. In Section 2.3 of this paper, based on relevant standard specifications and by referencing some existing research achievements, all the indicator evaluation levels were divided into five levels, and their corresponding level criteria were determined. Therefore, when N = 5, the degree of association function [30] can be represented as follows:

$${\mathsf{\mu }}_{\mathrm{i}1}=\left\{\begin{array}{l}1 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},1}\right)\\ 1 - \frac{2\left({\mathrm{x}}_{\mathrm{i}}-{\mathrm{p}}_{\mathrm{i},1}\right)}{{\mathrm{p}}_{\mathrm{i},2}-{\mathrm{p}}_{\mathrm{i},1}} \hspace{1em} \left({\mathrm{p}}_{\mathrm{i},1}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},2}\right)\\ -1\hspace{1em} \hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{x}}_{\mathrm{i}}>{\mathrm{p}}_{\mathrm{i},2}\right)\end{array}\right.$$

(13)

$${\mathsf{\mu }}_{\mathrm{i}2}=\left\{\begin{array}{l}1 - \frac{2\left({\mathrm{p}}_{\mathrm{i},1}-{\mathrm{x}}_{\mathrm{i}}\right)}{{\mathrm{p}}_{\mathrm{i},1}-{\mathrm{p}}_{\mathrm{i},0}}\hspace{1em}\hspace{1em}\left({\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},1}\right) \\ 1\hspace{1em} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{p}}_{\mathrm{i},1}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},2}\right)\\ 1 - \frac{2\left({\mathrm{x}}_{\mathrm{i}}-{\mathrm{p}}_{\mathrm{i},2}\right)}{{\mathrm{p}}_{\mathrm{i},3}-{\mathrm{p}}_{\mathrm{i},2}}\hspace{1em}\hspace{1em}\left({\mathrm{p}}_{\mathrm{i},2}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},3}\right) \\ -1 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{x}}_{\mathrm{i}}>{\mathrm{p}}_{\mathrm{i},3}\right)\end{array}\right.$$

(14)

$${\mathsf{\mu }}_{\mathrm{i}3}=\left\{\begin{array}{l}-1 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},1}\right) \\ 1 - \frac{2\left({\mathrm{p}}_{\mathrm{i},2}-{\mathrm{x}}_{\mathrm{i}}\right)}{{\mathrm{p}}_{\mathrm{i},2}-{\mathrm{p}}_{\mathrm{i},1}}\hspace{1em}\hspace{1em}\left({\mathrm{p}}_{\mathrm{i},1}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},2}\right)\\ 1\hspace{1em} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{p}}_{\mathrm{i},2}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},3}\right) \\ 1 - \frac{2\left({\mathrm{x}}_{\mathrm{i}}-{\mathrm{p}}_{\mathrm{i},3}\right)}{{\mathrm{p}}_{\mathrm{i},4}-{\mathrm{p}}_{\mathrm{i},3}}\hspace{1em}\hspace{1em}\left({\mathrm{p}}_{\mathrm{i},3}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},4}\right)\\ -1 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{x}}_{\mathrm{i}}>{\mathrm{p}}_{\mathrm{i},4}\right)\end{array}\right.$$

(15)

$${\mathsf{\mu }}_{\mathrm{i}4}=\left\{\begin{array}{l}-1 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},2}\right) \\ 1 - \frac{2\left({\mathrm{p}}_{\mathrm{i},3}-{\mathrm{x}}_{\mathrm{i}}\right)}{{\mathrm{p}}_{\mathrm{i},3}-{\mathrm{p}}_{\mathrm{i},2}}\hspace{1em}\hspace{1em}\left({\mathrm{p}}_{\mathrm{i},2}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},3}\right)\\ 1\hspace{1em} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{p}}_{\mathrm{i},3}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},4}\right) \\ 1 - \frac{2\left({\mathrm{x}}_{\mathrm{i}}-{\mathrm{p}}_{\mathrm{i},4}\right)}{{\mathrm{p}}_{\mathrm{i},5}-{\mathrm{p}}_{\mathrm{i},4}}\hspace{1em}\hspace{1em}\left({\mathrm{p}}_{\mathrm{i},4}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},5}\right)\end{array}\right.$$

(16)

$${\mathsf{\mu }}_{\mathrm{i}5}=\left\{\begin{array}{l}-1 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},3}\right)\\ 1 - \frac{2\left({\mathrm{p}}_{\mathrm{i},4}-{\mathrm{x}}_{\mathrm{i}}\right)}{{\mathrm{p}}_{\mathrm{i},4}-{\mathrm{p}}_{\mathrm{i},3}}\hspace{1em}\hspace{1em}\left({\mathrm{p}}_{\mathrm{i},3}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},4}\right)\\ 1\hspace{1em} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left({\mathrm{p}}_{\mathrm{i},4}<{\mathrm{x}}_{\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i},5}\right)\end{array}\right.$$

(17)

In the equation, x_i represents the measured value of the indicator, and the degree of association for the indicator i with the five levels are denoted as μ_i1, μ_i2, μ_i3, μ_i4, μ_i5, respectively. The calculation formulas given in Equations (13)–(17) are applicable for cost-type indicators, where the risk decreases as the indicator value decreases, that is, p_i,1 < p_i,2 < p_i,3 < p_i,4 < p_i,5. In the risk assessment process, there is another type of indicator known as benefit-type indicators, where the risk decreases as the indicator value increases. In this case, the ordering of the level criteria is reversed compared to the cost-type indicators. Specifically, it follows the pattern p_i,1 > p_i,2 > p_i,3 > p_i,4 > p_i,5.

3.3.2. Membership Level Determination

Formulas (13) to (17) yield the single-indicator degrees of association for each reference level. To assess the operational safety risk of a large tunnel on a highway, it is necessary to calculate the comprehensive degree of association for each reference level by combining the comprehensive weights of each indicator with its single-indicator degree of association. The calculation formula for the comprehensive degree of association is given in Formula (18). According to the principle of maximum membership degree, the risk level corresponding to the maximum value of the comprehensive degree of association among all levels is considered the assessed risk level for the sample.

$${\mathsf{\mu }}_{\mathrm{k}}={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathsf{\mu }}_{\mathrm{ik}}}{\mathrm{w}}_{\mathrm{i}}$$

(18)

In the equation, μ_k represents the comprehensive degree of association corresponding to level k, where μ_k ∈ [0, 1]. The symbol w_i represents the weight of indicator i.

4. Engineering Case Analysis

Taking the example of three large tunnels in the K0 + 000 to K46 + 920 section of the G1523 Yongguan Expressway (specific data can be found in

Table 4. Summary of the data for the large tunnels in the surveyed road section.

Serial Number	Tunnel Names	Start and End Stationing	Length (m)	Tunnel Alignment		Number of Accidents
				Slope (%)	Horizontal Curve Alignment
1	Sijiao’an Tunnel	K2 + 748~K4 + 140	1392	0.50	Circular Curve + Transition Curve + Straight Segment	84
2	Jiaodong’ao Tunnel	K7 + 660~K9 + 815	2155	−2.13, 2.5	Straight Segment + Circular Curve	103
3	Anjishan Tunnel	K37 + 086~K38 + 410	1324	−1.49, 0.5	Circular Curve + Transition Curve + Straight Segment	10

), the operational safety risk of the large tunnels will be assessed using both the Triangular Fuzzy Analytic Hierarchy Process (FAHP) and the traditional Analytic Hierarchy Process (AHP).

Based on the assessment indicator system determined in Section 2.2, this paper invited peer experts who have relatively good knowledge of the operational conditions of large tunnels on the highways in Zhejiang Province, China, to participate in a questionnaire survey. A total of 40 questionnaires were distributed to design institute senior engineers, university professors, technical professionals, and operations management personnel via email or paper format. All 40 questionnaires were received, and after screening, 24 valid questionnaires were selected for analysis.

4.1. Determination of Evaluation Index Weights

In this survey, two questionnaire survey methods described in this study were employed to collect expert opinions. Subsequently, the Triangular Fuzzy Analytic Hierarchy Process (FAHP) and the traditional Analytic Hierarchy Process (AHP) were used to determine the weights of evaluation indicators. As an example, the weights of evaluation indicators were calculated using the two assessment methods for the Sijiao’an Tunnel, and the results are presented in

Table 5. Comprehensive weights of indicators.

Criteria Layer	Indicator Layer		Weighting (AHP)		Weighting (FAHP)
	Entrance Section	Middle Section	Entrance Section	Middle Section	Entrance Section	Middle Section
Tunnel condition	Skid resistance performance of road surfaces U11	Technical condition of road surfaces U11	0.132	0.025	0.087	0.030
	Tunnel portal geometry U12	Minimum radius of planar curve U12	0.128	0.030	0.093	0.045
	Maximum slope U13	Maximum slope U13	0.065	0.051	0.055	0.049
	Civil engineering structural techniques U14	Civil engineering structural techniques U14	0.030	0.011	0.050	0.003
	Electromechanical facilities technical condition U15	Electromechanical facilities technical condition U15	0.066	0.020	0.087	0.022
	Technical condition of other facilities U16	Technical condition of other facilities U16	0.022	0.012	0.009	0.005
	/	Cross passages and emergency stopping lanes U17	/	0.028	/	0.029
		Tunnel length U18		0.046		0.032
Traffic characteristics	Operating speed U21	Operating speed U21	0.047	0.057	0.085	0.051
	Coordinated nature of operating speeds U22	Coefficient of variation of vehicle speed U22	0.145	0.122	0.116	0.108
	Service level U23	Service level U23	0.042	0.079	0.062	0.073
	Proportion of large vehicles U24	Proportion of large vehicles U24	0.073	0.075	0.069	0.090
	Overload ratio U25	Overload ratio U25	0.044	0.040	0.049	0.031
Operational environment	CO concentration U31	CO concentration U31	0.012	0.048	0.003	0.058
	Visibility U32	Visibility U32	0.029	0.068	0.034	0.074
	Luminance U33	Luminance U33	0.035	0.097	0.036	0.074
	Noise decibel value U34	Noise decibel value U34	0.010	0.024	0.020	0.039
	Proportion of adverse weather U35	Proportion of adverse weather U35	0.034	0.016	0.024	0.010
Operational management	Organizational structure U41	Organizational structure U41	0.008	0.014	0.008	0.020
	Regulations and procedures U42	Regulations and procedures U42	0.008	0.014	0.021	0.035
	Publicity and education U43	Publicity and education U43	0.012	0.014	0.027	0.013
	Emergency management U44	Emergency management U44	0.026	0.066	0.035	0.059
	Traffic management U45	Traffic management U45	0.033	0.046	0.032	0.051

.

4.2. Determination of Safety Risk Level

The evaluation team conducted on-site field surveys of the surveyed tunnels and communicated and exchanged information with safety managers from relevant organizations. They gained an understanding of the segments within the evaluated tunnels that are prone to accidents and the current state of operation and management. Additionally, they collected various materials, including design drawings, management systems, emergency plans, structural condition management records, and maintenance and rectification records. After categorizing and organizing the above data, specific scores for each indicator in the risk assessment index system for each evaluated object were determined. The compiled indicator assessment scores are presented in

Table 6. Evaluation indicator scores for Sijiao’an Tunnel.

Criteria Layer	Indicator Layer		Evaluation Method	Indicator Value
	Entrance Section	Middle Section		Entrance Section	Middle Section	Exit Section
Tunnel condition	Skid resistance performance of road surfaces U11	Technical condition of road surfaces U11	Information search and on-site inspection	64.6	87	68.2
	Tunnel portal geometry U12	Minimum radius of planar curve U12	Information search	148	1500	140
	Maximum slope U13	Maximum slope U13	Information search	0.5	0.5	0.5
	Civil engineering structural techniques U14	Civil engineering structural techniques U14	Information search and on-site inspection	78.5	78.7	80.0
	Electromechanical facilities technical condition U15	Electromechanical facilities technical condition U15	Information search and on-site inspection	98	98	98
	Technical condition of other facilities U16	Technical condition of other facilities U16	Information search and on-site inspection	86	86	86
	/	Cross passages and emergency stopping lanes U17	Information search	-	90	-
		Tunnel length U18			1392
Traffic characteristics	Operating speed U21	Operating speed U21	On-site testing	18.9	4.8	7.7
	Coordinated nature of operating speeds U22	Coefficient of variation of vehicle speed U22	On-site testing and model prediction	13.2	0.11	2.9
	Service level U23	Service level U23	Information search	0.44	0.44	0.44
	Proportion of large vehicles U24	Proportion of large vehicles U24	Information search	6.04%	6.04%	6.04%
	Overload ratio U25	Overload ratio U25	Information search	2%	2%	2%
Operational environment	CO concentration U31	CO concentration U31	Information search and on-site inspection	47	62	53
	Visibility U32	Visibility U32	Information search and on-site inspection	5.2	6.0	5.2
	Luminance U33	Luminance U33	Information search and on-site inspection	11.7	5.5	11.0
	Noise decibel value U34	Noise decibel value U34	Information search and on-site inspection	81	93	83
	Proportion of adverse weather U35	Proportion of adverse weather U35	Information search	47.4%	47.4%	47.4%
Operational management	Organizational structure U41	Organizational structure U41	Information search and interviews	90	90	90
	Regulations and procedures U42	Regulations and procedures U42	Information search and interviews	90	90	90
	Publicity and education U43	Publicity and education U43	Information search and interviews	85	85	85
	Emergency management U44	Emergency management U44	Information search and interviews	74	74	74
	Traffic management U45	Traffic management U45	Information search and interviews	80	80	80

.

The individual indicator membership degrees to each level were determined using Equations (13)–(17). Then, based on Equation (18) and in conjunction with the indicator weights shown in Table 5, the comprehensive membership degrees corresponding to each indicator for the five levels were separately established. According to the principle of maximum membership degree, the level corresponding to the maximum comprehensive membership degree is considered the risk level for each section of the Sijiao’an Tunnel. By following the same method and process as described above for determining the risk levels, the risk levels for each section of the three long and large tunnels within the G1523 Yongguan Expressway (Section K0 + 000 to K46 + 920) can be obtained, as shown in

Table 7. Risk Assessment Results for Long Tunnels in the G1523 Yongguan Expressway (Section K0 + 000 to K46 + 920).

Tunnel Names	The Risk Level Assessment Results for Each Section of the Tunnel
	The Traditional Analytic Hierarchy Process (AHP)			The Fuzzy Analytic Hierarchy Process (FAHP)
	Entrance Section	Middle Section	Exit Section	Entrance Section	Middle Section	Exit Section
Sijiao’an Tunnel	II	II	I	II	II	II
Jiaodong’ao Tunnel	III	II	II	III	II	II
Anjishan Tunnel	II	I	I	II	I	II

:

The highest risk level among the risk levels in each section is selected as the overall risk level of the entire tunnel. The risk levels determined by the two methods of calculating indicator weights (Triangular FAHP and Traditional AHP) for the overall tunnel risk level are found to be very similar, with negligible differences.

4.3. Comparative Analysis of Evaluation Results

To demonstrate the effectiveness of the Triangular Fuzzy Analytic Hierarchy Process (FAHP) method, this paper conducts a comparative analysis between the comprehensive weights of evaluation indicators and the evaluation results obtained from the Traditional Analytic Hierarchy Process (AHP) method, and the results obtained from the Triangular Fuzzy Analytic Hierarchy Process (FAHP) method.

(1) The comparison results between Figure 10 and Figure 11 show differences in the comprehensive weights of the evaluation indicators at the sub-criteria level determined by the two methods. The magnitude of these differences varies for different indicators. Considering that the two methods employed different questionnaire survey methods, matrix determination approaches, and were influenced by subjective errors from different experts, the differences in weights are a normal outcome resulting from the combination of multiple factors. Furthermore, the relative changes in comprehensive weights of evaluation indicators obtained using the Triangular Fuzzy Analytic Hierarchy Process (FAHP) and the traditional AHP show a basic consistency in their trends. Overall, they exhibit similarities, and the indicators ranked among the top few in importance at the sub-criteria level are the same. Although there might be some differences in the order, the results still effectively reflect the main risk characteristics of the evaluated objects.

Furthermore, during the practical calculation, it was observed that the judgment matrices determined using the traditional questionnaire survey method often failed to pass the consistency test. They required repeated adjustments to meet the consistency requirements. On the other hand, the simplified triangular fuzzy judgment matrices determined based on the expert system analysis method generally met the consistency requirements quite well. Therefore, overall, the use of the expert system analysis method to determine the judgment matrices is more intuitive and applicable. The weights of the indicators obtained from the triangular fuzzy analytic hierarchy process are consistent with the expert opinions reflected by the weights obtained from the traditional analytic hierarchy process. This also validates the rationality and effectiveness of using the expert system analysis method to collect expert opinions and determine the weights of evaluation indicators based on the triangular fuzzy analytic hierarchy process in this paper.

(2) From Figure 12, it can be observed that the distribution of risk levels in different sections of the tunnel indicates that the overall risk levels determined by both methods are consistent. Among them, the Triangle Fuzzy Analytic Hierarchy Process (FAHP) method determined the risk level of the exit section of Sijiao’an Tunnel as Level II and the risk level of the exit section of Anjishan Tunnel as Level II as well. Both of these levels are one level higher than the risk levels determined by the traditional Analytic Hierarchy Process (AHP) method. From a safety perspective, the evaluation method adopted in this study yields tunnel partition risk levels that are more conservative and safety-oriented.

5. Conclusions

The operational safety situation of long and large highway tunnels is severe. In this study, a partitioned assessment index system for evaluating the operational safety risk of long and large highway tunnels was constructed from the perspective of risk management. To address the challenges of the traditional AHP method, such as obtaining expert opinions quickly and effectively and dealing with strong subjectivity and bias, this paper proposes the adoption of the Triangular Fuzzy Analytic Hierarchy Process (FAHP) to determine the weights of the evaluation indicators for tunnel operational safety risk. Additionally, the paper combines the Triangular FAHP with Set Pair Analysis to construct a risk assessment model for the operational safety of long and large highway tunnels. The advantages of this approach are as follows:

(1)

Introducing a new expert system analysis method to collect expert opinions and proposing a new fuzzy number determination method for transforming expert opinions. This process is simple and clear, effectively simplifying the tedious and time-consuming pairwise comparison scoring process in expert questionnaires. Moreover, the judgment matrix determined by this method can better satisfy the consistency requirements.

(2)

The Triangular Fuzzy Analytic Hierarchy Process (FAHP) employs triangular fuzzy numbers instead of single values to express expert opinions, considering the influence of different perspectives among decision-makers and reflecting the ambiguity and uncertainty inherent in the expert judgment process. This approach better aligns with the real-world decision-making scenario of experts and makes the risk assessment results more reasonable and well-founded.

(3)

By establishing a tunnel operational safety risk assessment model based on the Triangular Fuzzy Analytic Hierarchy Process (FAHP) and Set Pair Analysis (SPA), the similarity between the indicator set and the standard set is compared using Set Pair Analysis. This ultimately achieves a combination of subjective weighting and objective evaluation, improving the accuracy of risk assessment for the operational safety of long and large highway tunnels.

Using the long and large tunnels within the G1523 Yongguan Expressway section from K0 + 000 to K46 + 920 as an engineering example, a comparative evaluation was conducted using both the Triangular Fuzzy Analytic Hierarchy Process (FAHP) and the traditional AHP. The results revealed that the trend of evaluation indicator weights determined by the Triangular FAHP was essentially consistent with the results obtained from the traditional AHP. The tunnel risk levels determined based on the Triangular Fuzzy Analytic Hierarchy Process (FAHP) align with the actual operational safety status of the tunnels. Moreover, the risk levels assessed by the Triangular FAHP are relatively more conservative compared to the results obtained from the traditional AHP. This demonstrates the rationality and accuracy of the proposed risk assessment method for the operational safety of long and large highway tunnels in this study. By conducting a detailed analysis of the operational safety risk assessment results, identifying the causes of problems and weak points in operational management, and proposing targeted corrective measures, timely resolution of safety hazards in long and large highway tunnels can be achieved. This continuous improvement in risk management will help reduce the occurrence of safety accidents in long and large highway tunnels.

However, the evaluation method proposed in this study still has limitations. The risk assessment method presented in the paper is still in the research stage and requires extensive practical experimentation for continuous validation and refinement. Further validation through practical applications and experiments is necessary to enhance its reliability and effectiveness. Additionally, the tunnel operational safety risk assessment index system selected in this study may not be comprehensive enough. The rationality of the division of grading standards for each evaluation indicator also requires further validation. Certainly, to increase the practical applicability and real-world value of this research, the next step could involve developing the evaluation method into an easy-to-use assessment software that can be applied in engineering practice. Indeed, further consideration could be given to conducting a cost-benefit analysis of implementing control measures for different risk levels in tunnels. This would involve establishing a database of risk control measures corresponding to different risk levels in long and large highway tunnels. Once the risk level is determined, tunnel operation management units can directly access the database to find targeted and cost-effective control measures to mitigate the identified risks. This approach would enhance the efficiency and effectiveness of risk management in tunnel operations while optimizing resource allocation for safety improvement measures.